Graph this system of Inequalities?

[SunshineAlgebra]

HI! I am having rotten luck with this homework question:

12) Graph this system of inequalities.
(x+2)^2 + (y-1)^2 < 16
2y<= x + 6

I figured out the simple part (2y <= x + 6) and did this work:
2y <= x +6
2y = 0 +6
2y = 6
y = 3

2(0) = x + 6
0 = x + 6
-6 = x

And I drew the line on the graph.

I tried to solve the hard part (x + )^2 + (y - 1)^2 < 16, but I don't get far with it.
(y - 1)^2 = 16 - (x + 2)^2
y^2 - 1 = 4 - x^2 + 4
y = 1 - x
??

My work is completely wrong. I looked for a sample problem in my book, but I couldn't find one... PLEASE HELP! I have the final exam on Tuesday!

 

[wjm11]

12) Graph this system of inequalities.
(x+2)^2 + (y-1)^2 < 16
2y<= x + 6

I figured out the simple part (2y <= x + 6) and did this work:
2y <= x +6
2y = 0 +6
2y = 6
y = 3

2(0) = x + 6
0 = x + 6
-6 = x

And I drew the line on the graph.

I tried to solve the hard part (x + )^2 + (y - 1)^2 < 16, but I don't get far with it.
(y - 1)^2 = 16 - (x + 2)^2
y^2 - 1 = 4 - x^2 + 4

For the line equation, it looks like you solved for the x and y intercepts correctly, though I can't see how you graphed them. Another approach for the line is to put it into slope-intercept form:

2y<= x + 6
y <= (1/2)x + 3

So the line passes through (0,3) and has a slope of 1/2. Since there is a "y <", we shade under the line. (Place your pencil on the line and move down.)

For the other part, (x+2)^2 + (y-1)^2 < 16, it is necessary to recognize that this is a circle with center (-2,1) and radius 4. Draw the circle with a dotted line since there is now"=" sign. Shade inside the circle since the x^2 and y^2 part is "<" 16. [Note: you did not FOIL correctly when attempting to expand the squared terms.]

For info on circles, see:

http://www.purplemath.com/modules/circle.htm